In recent years, there are substantial demands to reduce packet loss in the Internet. Among the schemes proposed, finding backup paths in advance is considered to be an effective method to reduce the reaction time. Very commonly, a backup path is chosen to be a most disjoint path from the primary path, or in the network level, backup paths are computed for all links (e.g., IPRFF). The validity of this straightforward choice is based on 1) all the links may fail with equal probability; and 2) facing the high protection requirement today, having links not protected or sharing links between the primary and backup paths just simply look weird. Nevertheless, indications from many research studies have confirmed that the vulnerability of the links in the Internet is far from equality. In addition, we have seen that full protection schemes may introduce high costs . In this paper, we argue that such approaches may not be cost effective. We first analyze the failure characteristics based on real world traces from CERNET2, the China Education and Research NETwork 2. We observe that the failure probabilities of the links is heavy-tail, i.e., a small set of links caused most of the failures. We thus propose a selective protection scheme. We carefully analyze the implementation details and the overhead for general backup path schemes of the Internet today. We formulate an optimization problem where the routing performance (in terms of network level availability) should be guaranteed and the backup cost should be minimized. This cost is special as it involves computation overhead. Consequently, we propose a novel Critical-Protection Algorithm which is fast itself. We evaluate our scheme systematically, using real world topologies and randomly generated topologies . We show significant gain even when the network availability requirement is 99.99% as compared to that of the full protection scheme.